Teaching According to Students'Aptitude: Personalized Mathematics Tutoring via Persona-, Memory-, and Forgetting-Aware LLMs

2025-11-19

AI Summary

Existing LLM-based intelligent tutoring systems struggle to model the dynamic evolution of student knowledge—such as shifting competencies, conceptual gaps, and forgetting patterns—resulting in coarse-grained personalization and weak adaptivity. To address this, we propose the first LLM-powered mathematical tutoring framework integrating learner persona modeling, event-based memory mechanisms, and a continuous forgetting curve for fine-grained, real-time tracking of student knowledge states. Our approach leverages knowledge tracing–informed forgetting modeling, structured learner profiling, difficulty-aware prompt engineering, and LLM-augmented collaborative generation to enable adaptive problem recommendation and stepwise explanation. Experiments demonstrate statistically significant improvements over state-of-the-art baselines in learning gain and pedagogical alignment, validating the technical efficacy and educational value of deeply embedding cognitive forgetting mechanisms and multidimensional learner representations into LLM-based tutoring systems.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Data Mining & Knowledge Management: Conversational Systems for Recommendation & Retrieval

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Large Language Models (LLMs) are increasingly integrated into intelligent tutoring systems to provide human-like and adaptive instruction. However, most existing approaches fail to capture how students'knowledge evolves dynamically across their proficiencies, conceptual gaps, and forgetting patterns. This challenge is particularly acute in mathematics tutoring, where effective instruction requires fine-grained scaffolding precisely calibrated to each student's mastery level and cognitive retention. To address this issue, we propose TASA (Teaching According to Students'Aptitude), a student-aware tutoring framework that integrates persona, memory, and forgetting dynamics for personalized mathematics learning. Specifically, TASA maintains a structured student persona capturing proficiency profiles and an event memory recording prior learning interactions. By incorporating a continuous forgetting curve with knowledge tracing, TASA dynamically updates each student's mastery state and generates contextually appropriate, difficulty-calibrated questions and explanations. Empirical results demonstrate that TASA achieves superior learning outcomes and more adaptive tutoring behavior compared to representative baselines, underscoring the importance of modeling temporal forgetting and learner profiles in LLM-based tutoring systems.

Problem

• Modeling dynamic knowledge evolution in student learning processes
• Addressing forgetting patterns and proficiency gaps in mathematics tutoring
• Calibrating instructional scaffolding to individual mastery levels

Innovation

• Persona-aware LLMs for student proficiency modeling
• Memory tracking with continuous forgetting curve integration
• Dynamic knowledge tracing for difficulty-calibrated question generation